(CNN) -- Almost from the moment Laci Peterson was reported missing on Christmas Eve 2002, police said, a combination of red flags and a gut feeling that things were not right drove their investigation in the direction of her husband, Scott.

The patrol officer who responded to the Peterson home noticed a number of oddities. For instance, things did not square with Scott Peterson's tale of a fishing trip, said Modesto Police Detective Al Brochini at a news conference Thursday.

Chief among those was Peterson's demeanor, given the fact his eight-months-pregnant wife was missing.

"All along, he had a very nonchalant, going-through-the-motions kind of attitude with me," Brochini said. "His major concerns were not Laci in the beginning of the case."

Instead, Brochini said, Peterson had voiced concerns about a car door hitting another and the condition of furniture.

Another Modesto Police detective Jon Buehler cited a sugary phone message left by Peterson, ostensibly for Laci but really meant for police to hear, which Buehler said would have seemed odd for anyone married for a while.

Peterson, 32, was convicted in November of killing Laci and the couple's unborn son. Jurors recommended he receive the death penalty, and a judge followed that recommendation Wednesday.

On Thursday, Peterson was transferred from San Mateo County Jail to the infamous San Quentin State Prison, where he will likely be put to death when that day comes.

Peterson's demeanor and lack of emotion were the first red flag, authorities said, and they continued through his sentencing.

"That's been his reaction since the first day I met him," Brochini said. "Cool. Calm. Nonchalant. Polite. Arrogant. Thinks he's smarter than everybody. That's how he acted yesterday."

Buehler said he believes Peterson misjudged the police and the media coverage of the case. It became a joke, he said, that detectives with only high-school diplomas and a little bit of college could bring down a guy with a four-year degree from California Polytechnic Institute.

Prosecutors said they would "definitely" have charged Peterson in his wife's death, even if her torso and the body of their son had not washed up on shore in April 2003.

"It's a culmination of circumstantial evidence," prosecutor David Harris said. "Each piece maybe doesn't make the case, but when you put it all together, it makes sense. Even without the body, there was plenty of evidence to prove a homicide was committed and he was responsible."

And when Peterson's mistress, Amber Frey, came forward to assist police, it was "huge," Buehler said. "In the early days, the information she had gave us some direction. ... Amber never went sideways on this once. We couldn't have asked for a better witness."

And the audiotapes she made of her phone calls with Peterson were crucial as well, Harris said. "The jury got to hear that he wasn't what anybody saw. ... This is a person who's lying to the police, who wasn't being cooperative with the investigation."

Laci's family members had been planning to attend the Thursday news conference, said Kim Petersen of the Sund/Carrington Foundation, which has assisted the family, but after Peterson's emotional sentencing Wednesday, "they are exhausted today, both emotionally and physically."

Modesto Police Chief Roy Wasden said he does not plan to attend Peterson's execution, should it occur in his lifetime.

"For me, the statement has been made," he said. "This is a domestic violence homicide. It's not acceptable in our society to kill your spouse. If you're in a relationship and it's not working, use resources. Don't use violence. I think it's a worthwhile message to carry out of this tragedy."